Given that,
AB ‖ DE and EC ‖ EF
To prove:
∠ABC = ∠DEF
Construction:
Produce BC to X such that it intersects DE at M
Proof: Since,
AB ‖ DE and BX is the transversal
Therefore,
∠ABC = ∠DMX (Corresponding angles) (i)
Also,
BX ‖ EF and DE is transversal
Therefore,
∠DMX = ∠DEF (Corresponding angles) (ii)
From (i) and (ii), we get
∠ABC = ∠DEF
Hence, proved